The present invention provides for a compressible grout mix for filling an annular gap between a tunnel rock wall surface and a tunnel liner of a tunnel in a rock formation subject to time dependent deformation after excavation and a method of filling the annular gap between a tunnel rock wall surface and a tunnel liner of a tunnel in a rock formation subject to time dependent deformation after excavation utilizing the compressible grout mix for resilient absorption of forces in the hardened state of the compressible grout mix exerted by the time dependent deformation of the rock wall surface into the tunnel opening. The method includes:a. providing the compressible grout mix comprising hydraulic binding agent, bentonite clay, polymer foam particles, water-reducing admixture, water and air,b. placing the compressible grout mix in the annular gap between the tunnel wall rock surface and the tunnel liner, andc. allowing the compressible grout mix to set, wherein the compressible grout mix in the hardened state has a compressible ratio greater than the anticipated time dependent deformation.